1. Department of Chemical Engineering, National Chung Cheng University
A Theoretical and Experimental Investigation on Short-Time Stretch Relaxation of Entangled Polymer Solutions
Y. H. Wen (溫玉合) and C. C. Hua (華繼中)
Department of Chemical Engineering, National Chung Cheng University

2. Introduction Historical Sketch
de Gennes (1971)
Doi and Edwards (1986)
The tube (or reptation) model and its derivatives have proven very successful, especially in describing the linear viscoelasticity of entangled polymer liquids
Linear
relaxation

3. A Story about Nonlinear Viscoelasticity
Chain Retraction
(nonlinear relaxation)
Chain Retraction
(nonlinear relaxation)
Orientation Relaxation
(linear relaxation)
PS/DEP solution (Mw=5.5x106 g/mol; PI=1.01; Zeq=77)

4. Application of the Rouse chain in two distinct cases
Only terminal chain retraction is captured for the case of concentrated systems
Rouse chain
Dilute solution
Concentrated solution
Objectives of the current investigation:
The Rouse Model Prediction on
Short-time Chain Retraction
Nonlinear Stress
Relaxation Data in
Single-step Strain Flows
For time scales <
The impact of polymer entanglement ?

5. Formulation of Stress Relaxation in Single-Step Strain Flows
Nonlinear stress relaxation modulus:
: shear stress
: tube survival probability
: strain
: dimensionless chain stretching
: plateau modulus
: D-E universal function
(w/o IA assumption)
The Rouse model
where and
: No. of Rouse modes
: No. of entanglements per chain at equilibrium

6. Experimentally Determined Model Parameters
PS/TCP solution
Number of entanglements per chain at equilibrium,
φ: volume fraction of polymer
The Rouse time,

7. Theory/Data Comparisons
PS/DEP solution
PS/DEP solution

8. (a) t = 0 (at equilibrium) A Renormalized Rouse model:
Self-consistently Renormalized Rouse Modes
(a) t = 0 (at equilibrium)
A different number of
entanglements per chain
 N is a dynamic variable
Stretching
(b) t = 0+
A Renormalized Rouse model:
Retraction
(c) t <
where

9. PS/DEP solution
PS/DEP solution

10. Theory/Data Comparisons for Various Polymer Species
PS/TCP solution
PαMS/PCB solution
1,4-PB/FO solution
PMMA/PCB solution

11. Conclusions
The instantaneous entanglement property has a significant impact on short-time chain retraction of entangled polymer solutions.
Self-consistent mode renormalization leads to better agreement with experimental data.
Remaining discrepancies might result from
(a) Inaccuracy of short-time relaxation data and/or
(b) Tube pressure associated with a deformed polymer network

12. Acknowledgements National Science Council
Excellency Project of the Ministry of Education of ROC
(91-E-FA04-2-4A)